Comparison Between Classical Kelvin-Voigt Model And Fractional Kelvin-Voigt Model For Numerical Simulation Of Pmma Viscoelasticity Based On Beinstein Polynomial Algorithm

In recent years,viscoelastic materials are widely used in aerospace,construction,mechanical engineering and other fields.With the introduction of advanced viscoelastic materials,their research value is increasing.Viscoelastic constitutive relation and viscoelastic beam can well describe the mechanical properties of viscoelastic materials.Based on this,this paper uses Bernstein polynomials algorithm to solve the bending models of two kinds of viscoelastic beams in time domain and compares the integer order and fractional order constitutive models,and studies the prediction ability of Kelvin Voigt model to the behavior of viscoelastic materials.Firstly,according to the definition and properties of traditional Fourier transform and fractional Fourier transform,and the relationship between composite modulus,storage modulus and loss modulus,the relationship between storage modulus and loss modulus and the parameters of integral order Kelvin Voigt constitutive model and fractional order Kelvin Voigt constitutive model is deduced.According to the experimental data,the optimal parameters of integral order Kelvin Voigt constitutive model and fractional order Kelvin Voigt constitutive model of viscoelastic are estimated,which lays a foundation for the numerical analysis of two kinds of viscoelastic beams.Secondly,according to the equations of motion,the constitutive relation of viscoelastic materials and the strain displacement relation,the integral order and fractional order vibration models of viscoelastic fixed beams are established,and the numerical solution is carried out by using Bernstein polynomial algorithm.Numerical examples show the displacement numerical solutions of the integral order and fractional order viscoelastic two end fixed beam constitutive models under different uniformly distributed loads,and the results are compared with the simulation values to verify the effectiveness of the algorithm,and the mechanical properties of viscoelastic materials are analyzed.Finally,the integral order model and the fractional order constitutive model of the viscoelastic cantilever are established in the time domain,and the differential operator matrix is derived by the Bernstein polynomials algorithm,and the numerical analysis is carried out.The numerical results show that the simulation results of the fractional order model are better than those of the integral order model,and the influence of the uniform load and the linear load on the displacement of the viscoelastic cantilever is studiedTo sum up,the integral order and fractional order models of the fixed beam and the cantilever beam are established in the time domain,and the Bernstein polynomials algorithm is used for numerical analysis.The numerical solution of displacement is compared with the simulation value to verify the effectiveness and practicability of the algorithm.